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# A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

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A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres

Feb 22, 2018

#1
+21978
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A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres

$$\begin{array}{|lcll|} \hline V_{\text{cylinder}} &=& \pi r^2\times 6r \\ &=& 6\pi r^3 \\\\ V_{\text{3\ spheres }} &=& 3\times \frac43\pi r^3 \\ &=& 4\pi r^3 \\\\ 1 - \dfrac{4\pi r^3}{6\pi r^3} \\\\ = 1 - \dfrac{2}{3} \\\\ = \dfrac{1}{3} \\ \hline \end{array}$$

$$\text{\frac13 of the cylinder is not filled by the spheres.}$$

Feb 22, 2018

#1
+21978
+1

A hollow cylinder has radius r cm and height 6r cm, 3 spheres, also of radius r cm, are put into the cylinder

work out the proportion of the cylinder NOT filled by the spheres

$$\begin{array}{|lcll|} \hline V_{\text{cylinder}} &=& \pi r^2\times 6r \\ &=& 6\pi r^3 \\\\ V_{\text{3\ spheres }} &=& 3\times \frac43\pi r^3 \\ &=& 4\pi r^3 \\\\ 1 - \dfrac{4\pi r^3}{6\pi r^3} \\\\ = 1 - \dfrac{2}{3} \\\\ = \dfrac{1}{3} \\ \hline \end{array}$$

$$\text{\frac13 of the cylinder is not filled by the spheres.}$$

heureka Feb 22, 2018